Advertisements
Advertisements
Question
Find the differential dy for the following functions:
y = `(1 - 2x)^3/(3 - 4x)`
Advertisements
Solution
dy = `[((3 - 4x)3(1 - 2x)^2(- 2) - (1 - 2x)^3(- 4))/(3 - 4x)^2] "d"x`
i.e., dy = `{(1 - 2x)^2/(3 - 4x)^2 [- 6(3 - 4x) + 4(1 - 2x)]} "d"x`
i.e., dy = `{(1 - 2x)^2/(3 - 4x)^2 [16x - 14]} "d"x`
= `2 ((8x - 7)(1 - 2x)^2)/(3 - 4x)^2 "d"x`
dy = `(2(8x - 7)(1 - 2x)^2)/(3 - 4x)^2 "d"x`
APPEARS IN
RELATED QUESTIONS
Use the linear approximation to find approximate values of `root(3)(26)`
Find a linear approximation for the following functions at the indicated points.
g(x) = `sqrt(x^2 + 9)`, x0 = – 4
Find a linear approximation for the following functions at the indicated points.
h(x) = `x/(x + 1), x_0` = 1
The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:
Relative error
Show that the percentage error in the nth root of a number is approximately `1/"n"` times the percentage error in the number
Find the differential dy for the following functions:
y = `"e"^(x^2 - 5x + 7) cos(x^2 - 1)`
Find df for f(x) = x2 + 3x and evaluate it for x = 3 and dx = 0.02
Find Δf and df for the function f for the indicated values of x, Δx and compare:
f(x) = x3 – 2x2, x = 2, Δx = dx = 0.5
Find Δf and df for the function f for the indicated values of x, Δx and compare:
f(x) = x2 + 2x + 3, x = – 0.5, Δx = dx = 0.1
Assuming log10 e = 0.4343, find an approximate value of Iog10 1003
Assume that the cross-section of the artery of human is circular. A drug is given to a patient to dilate his arteries. If the radius of an artery is increased from 2 mm to 2.1 mm, how much is cross-sectional area increased approximately?
A circular plate expands uniformly under the influence of heat. If its radius increases from 10.5 cm to 10.75 cm, then find an approximate change in the area and the approximate percentage change in the area
A coat of paint of thickness 0.2 cm is applied to the faces of cube whose edge is 10 cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube
Choose the correct alternative:
If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is
Choose the correct alternative:
The change in the surface area S = 6x2 of a cube when the edge length varies from x0 to x0 + dx is
Choose the correct alternative:
The approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is
Choose the correct alternative:
Linear approximation for g(x) = cos x at x = `pi/2` is
